Add lens projection system with balanced performance

ABSTRACT

An add lens projection system is designed such that substantially similar system performance is obtained with added and subtracted add lens elements at balanced positions on either side of a principal position at which the basic lens combination is designed. The basic lens combination may include a nonsymmetrical split dagor lens or a non-symmetrical heliar lens plus singlet.

United States P McCrobie June 26, 1913 [54] ADDIZENS PROJECTION SYSTEMWITH 2,985,070 5/1961 Lane 350/183 BALANCED PERFORMANCE FOREIGN PATENTSOF. APPLICATIONS Inventor: g z z Mccrobie, Rochester. 358,734 12/1921Germany 350/38 [73] Assignee: Xerox Corporation, Stamford, Conn. 'fEmmi""David Schonber! Assistant Examiner-Paul A. Sacher Filed: l 1971Attorney-James J. Ralabate, Albert A. Mahassel, Mi- [21] AWL 130,134chael Shanahan and Michael J. Colitz [52] U.S. Cl. 350/183, 350/38 [57]BSTRAC'I: 51 Int. Cl. 60211 15/10, G02b 7/04 add lens system des'gnedsuch that [58] Field in Search 350/38, 183,220 Substantially similarWfmman is mined with added and subtracted add lens elements at bal- 56 Rf Cue-d anced positions on either side of a principal position at 1UNITE]; $32 PATENTS which the basic lens combination is designed. Thebasic lens combination may include a non-symmetrical split 3283 3;: 3;350/220 dagor lens or a non-symmetrical heliar lens plus singlet.

e e 3,591,256 7/1971 Hoyer et a! 350/183 7 Claims, 4 Drawing Figures A1e .c t.

PRINCIPAL POSITION 7 2 4 5 s E-E 29 19 j I 22 I l; I 1 1 3. B 1,. l 1..A

BALANCED t /0 ADD LENS E 1 POSITION s s iii-:3 C .1.. if. BALANCED 9 ADDLENS POSITION wh \l c :1 A

PRINCIPAL POSITION 7 1 .!L a -1 BALANCED {ggwme ADD LENS E55; POSITION aPAIENIEDJUIZSISB 3.741.621

saw '1 0f 3 IA *i 8 Egg-5:51

" SIB I osmon INVENTOR GEORGE L. MC CROBIE ATTORNEY PAIENIEDmzs ma3.741.621

sumzura 5 4a 45 A42 A PRINCIPAL posmon v BALANCED 7 ADD LENS osmou l: :Iv r iL 39 J]. C w

BALANCED ADD LENS POSITION 1L 7 55 3 |c |A SIB ADD LENS PROJECTIONSYSTEM WITII BALANCED PERFORMANCE BACKGROUND OF THE INVENTION Thisinvention relates to heliar and split dagor lens systems and inparticular to lens systems of the foregoing types to which extra lenselements are added and subtracted to maintain a fixed overall conjugatelength and optical path while varying magnification.

Copying machines are often required to produce copies of an originaldocument or other target that are either enlarged or reduced in size.For the sake of economy in machine design, the overall conjugate lengthand optical path are preferably fixed and the lens elements aremanipulated to obtain the desired magnifications. An example of theforegoing type of optical system for a xerographic copying machine isdisclosed in US. Pat. No. 3,476,478. In the optical system described inthe patent, a main projection lens is moved along the optical axis andadd lens" elements are placed into the optical path at specifiedlocations to yield the different magnifications and maintain the overallconjugate. The disclosure of that patent is incorporated by referenceinto the present description. One problem encountered with add lensprojection systems is that the performance of the system falls off whenlens elements are added or subtracted from the basic lens combinationaround which the system is initially designed. For example, in thereferenced patent, the basic lens combination is designed for a 1:1magnification at a principal position and is moved to differentlocations at increasing distances from the principal position to obtainthe various magnifications. At the first removed or first add lensposition, the resolution capability of the lens system is less than atthe principal position and the aberrations are greater. This is anaturally expected result because the basic lens combination is tailormade for the principal position.

The deterioration in lens performance is even greater.

when the basic lens combination is moved to second, third and additionaladd lens positions. Consequently, although the desired magnificationsare obtained and the overall conjugate is held constant, the system maybe unacceptable at several add lens positions because resolution fallsoff too much and/or the aberrations become too large.

The present lens system optimizes the performance of add lens systems byincreasing the number of add lens positions, i.e., by increasing thenumber of magnifications available, without downgrading the lensperformance at new add lens positions.

Accordingly, it is an object of this invention to overcome the abovenoted problems and limitations associated with add lens" opticalsystems.

Another object of the present invention is to design an add lens systemhaving a plurality of add lens positions but a minimum of systemdeterioration due to shifting between add lens positions.

Yet another object of the invention is to define novel add lensprojection systems using heliar or split dagor lens combinations.

Another object of this invention is to balance the performance of an addlens system at various add lens positions.

Even a further object of this invention is to select, as between heliarand split dagor types, a basic lens combination for an add lens opticalsystem.

These and other objects of this invention are realized by designing anadd lens projection of system such that substantially similar systemperformance is obtained at two add lens positions. These equalperformance positions are on opposite sides of the principal positionmeaning that magnification is increased at one add lens position andreduced at the other, relative to the mag nification at the principalposition. Quite often a 1:1 magnification is desired and in the pastthis magnification was assigned to the principal position. One reasonfor this is to utilize symmetrical dagor, heliar, gauss, celor and otherlens systems which are substantially aberration free at the 1:1magnification. However, in this invention, the 1:1 magnification isassigned to an add lens position.

The present invention has application for systems requiring two or moremagnifications. In a two magnification system, the principal position isnot used but only the less efficient first and second add lenspositions. This is still advantageous because the performance of thelens system at the two add lens positions is balanced whereas it wouldbe unbalanced if, for example, the principal position and only one addlens position were used. In a three magnification system, the principaland flanking first and second add lens positions are all used. In a fourmagnification system, the principal position is not used and third andfourth add lens positions are created at further but balanced positionsfrom the principal position. In a five magnification system theprincipal position is used along with the other positions of the fourmagnification system. Greater even and odd numbers of magnification arepossible by creating more balanced add lens positions and by using ornot using the principal position. Also, an add lens position on one sideof the principal position can be balanced with two or more add lenspositions on the other side. In this case, the multiple add lenspositions are sufficiently close together, in terms of systemperformance, such that any one of them yield substantially similarsystem performance when compared to their balanced add lens position onthe opposite side.

The advantage gained by the present system is significant over a systemthat simply moves the basic lens combination further and further awayfrom the principal position without balancing. In a five magnificationsystem using the present scheme, only two drops in system performanceare encountered for the four positions added to the principal position.In prior art add lens systems, four drops in system performance wouldresult with four new lens positions. Clearly, a system might succeedwith only two deteriorating requests in performance made on its where itwould fail under four deteriorating requests.

DESCRIPTION OF THE DRAWINGS Other objects and features of the presentinvention will be apparent from a further reading of the presentspecification and from the drawings which are:

FIG. I is a schematic of a lens system according to the presentinvention employing a split dagor basic lens combination located at theprincipal position in part A and at balanced add lens positions in partsB and C.

' FIG. 2 is a schematic of a lens system according to the presentinvention employing a heliar plus singlet basic lens combination locatedat the principal position in part A and at balanced add lens positionsin parts B and C.

DESCRIPTION OF THE EMBODIMENTS The following discussion is limited tolens system design and the reader is referred to the disclosure of USPat. No. 3,476,478 for a specific application. That patent alsodiscloses apparatus for mounting the basic lens combination and addlens, for .moving the basic lens combination along the optical path andfor inserting and withdrawing an add lens. Naturally, the present addlens system will find application in that and other xerographic copyingmachines as well as in other nonxerographic machines such as those usingsilver halide photography as the recording medium. Furthermore, thedagor and heliar add lens systems of FIGS. 1 8r 2 are designed forspecific magnifications of about 1:1, 0.643X and 0.495X but quiteclearly other magnifications can be employed included those greater than121.

Turning now to FIG. I, the basic lens combination for this add lenssystem is the non-symmetrical split dagor lens 1 comprising the six lenselements 2-7 and centrally located aperture 8 The glass type, refractiveindex, curvature and spacing parameters for the dagor lens I are tailormade for about a 0.643X magnification at the principal position shown inpart A of FIG. 1. The system is designed using the GREY programdeveloped by David Grey associates, ACCOS developed by Gordon Spencer ofScientific Calculations, Inc. and the SCII" program developed atScientific Calculations. Analysis was done on UNIVAC 1108 and IBM 1 130Computers using the Scientific Calculations, Inc. GOALS" and SCIPprograms.

The design of the dagor lens at the 0.643X magnification is a departurefrom conventional practice. Conventional practice teaches that the basicdagor should be designed at the l :l magnification because the elemeritsleft and right of the aperture are symmetrical. The symmetry iseconomically desirable for production purposes and is qualitativelydesirable because coma and spherical and lateral aberrations are at aminimum. However, the non-symmetrical dagor is selected in thisinvention so that the principal position can be located between two addlens positions to balance" system performance.

In part B of FIG. 1, the basic lens combination 1 is moved to the firstadd lens position which is closer to the object plane 14 than theprincipal position thereby yielding an increase in magnification. Themagnification at this position is about 1:1. The doublet add lens 15 isaligned to the optical axis 16 at a fixed spacing from dagor lenselement 7. The doubletincludes the lens elements 17 and 18 which areselected to hold the overall conjugate and to correct lateral color inthe lens system with the basic lens combination at this position. Thedashed lines 29 indicate the withdrawn position of the doublet add lens25.

In part C of FIG. 1, the basic lens combination 1 is moved to the secondadd lens position which is closer to the image plane 24 than theprincipal position thereby yielding a reduction in magnification. Themagnification at the second add lens position is about 0.495X. Thedoublet add lens 15 is removed and the doublet add lens 25 is insertedin its place in alignment with the dagor lens 1 along the optical axesat a fixed spacing from dagor lens element 7. The doublet 25 includesthe lens elements 27 and 28 which are selected to correct lateral colorin the lens system at this second add lens position. (The dashed lines19 represent doublet 15 when it is at a withdrawn position.) The lenssystem at the principal position exhibits negligible lateral colorbecause the dagor is tailor made for that position.

The doublet add lenses I5 and 25 are designed such that the lens systemperforms substantially the same at the first and second add lenspositions. This is what is meant when the system is said to be balanced"at the two add lens positions. The balancing is accomplished by matchinglens system parameters such as depth of focus, resolution, andaberrations at the two add lens positions. The matching is possiblebecause in one case the basic lens combination is moved toward theobject and in theother it is moved toward the image. The fall off' inlens system performance decreases from the same starting point as thebasic lens is moved in the opposite directions. If the, basic lenscombination is moved to a first add lens position toward the object (orimage) and then to a second add lens position in the same direction, thedecrease in lens system performance falls off from a lower standard withthe second move thereby insuring that the lens system -performance willbe unbalanced at the two add lens positions.

The foregoing discussion should not be interpreted to mean that balanceis obtained by simply selecting add lens positions on opposite sides ofthe principal position. The spacing between add lens and basic lens,refractive index, glass type and curvature must be specifically selectedto obtain the balance. In fact, the add lenses are generally not similarbecause, for one, the basic lens element is not symmetrical.Consequently, to practice the present invention one must be aware of thedesired end result of balanced lens performance in addition to selectingadd lens positions on eitherside of the principal position.

Turning now to FIG. 2, the basic lens combination for this add lenssystem is the non-symmetrical heliar 41 plus the singlet 42. The heliarincludes the five lens elements 43-47 and aperture 48. The glass type,refractive index, curvature and spacing parameters for the heliar lens41 plus singlet 42 are tailor made for the 0.643X magnification at theprincipal position shown in part A OF FIG. 2. The design and analysisemployed include the same computer programs and computers as with thesplit dagor add lens system.

Again, the design of the heliar plus singlet lens at 0.643Xmagnification is a departure from conventional practice. As with thesplit dagor lens, conventional practice teaches that the basic lenscombination should be designed at the 1:1 magnification because theheliar is symmetrical at that magnification. The symmetry yields theeconomic and quality features mentioned earlier in regard to the dagorlens.

One difference between the present heliar and split dagor add lenssystems is that basically one less lens element is used in the heliarsystem. This one less" distinction assumes that other split dagorsystems are possible where singlet rather than doublet add lenses areused, such as where lateral color aberrations are not important tosystem design. Of course, the basic lens combination may alternatelyinclude a triplet, celor, full gauss, inverted gauss or other lenssystem. Another difference between the present two add lens systems isthat the heliar lens combination includes an additional lens element,i.e., the singlet 42, whereas in the split dagor system the dagor lensitself comprises the basic lens combination. This latter distinctionpoints out that the embodiment of FIG. 2 is even further removed fromconventional lens designs than the embodiment of FIG. 1. In fact, theheliar lens system of FIG. 2 exhibits superior performance'with greatereconomy than the split dagor of FIG. 1.

In part B of FIG. 2 the basic lens combination 41 is moved to the firstadd lens position which is closer to the object plane 14 than theprincipal position thereby yielding an increased magnification. Themagnification at this position is about 1:1 and is obtained by the newspacing and by removing the singlet 42 from the optical path. (The factthat a lens is subtracted from the basic lens combination at one of theadd lens position is also novel to add lens systems.) The dashed lines49 represent the withdrawn position of singlet 42.

In part C of FIG. 2, the basic lens combination 41 (minus singlet 42) ismoved to the second add lens position which is closer to the image plane24 than the principal position thereby yielding a reduction inmagnification. The magnification at this position is 0.495X and isobtained by the new location and by the substitution of singlet 55 forsinglet 42. Singlet 55 is aligned to the optical axis 16 and positionedat a specified distance from heliar element 47 substantially equal tothat for singlet 42. Dashed lines 49 and 59 represent the withdrawnpositions of the singlets 55 and 42 respectively. I

The heliar add lens system shows little lateral color aberration at theprincipal position since it is tailor made for that location. Unlike thesplit dagor system, however, the lateral color occurring at the firstand second (Ix and 0.495x) add lens positions does not require adoublet.

Another highly attractive feature of the heliar plus singlet system isthat one of the heliar elements 44 has a zero curvature meaning it iseconomical to manufacture. Also, the heliar plus singlet system has agreater depth of focus than the system of FIG. 1 which is highlyrelevant to production because of the wider mechanical tolerance that ispermitted.

The primary feature of the heliar system is still the same as that ofthe split dagor system; namely, balanced lens system performance at thefirst, second and other add lens positions. The balanced performance isobtained here as with the split dagor system by moving the basic lenscombination left and right of the principal position. The distancesactually moved and the parameters of the add lens added or subtracteddepend upon the magnification sought at the two add positions and thedegree of fall off in performance that is tolerable.

The following data defines the heliar plus singlet and split dagor addlens systems of FIGS. 1 and 2 and FIGS.

3 and 4 are enlarged schematics of the systems which help define thevarious parameters: These parameters include:

The lens element closest to the object plane I4 is designated I and alllens elements encountered proceeding toward the image plane 24 arelabeled similarly but with increasing numerical subscripts.

The air space between the object plane and lens element I is designatedS and all air spaces encountered proceeding toward the image plane arelabeled similarly but with increasing numerical subscripts.

The surface of lens element 1, closer to the object plane is labeled Iand all other lens element surfaces are labeled with increasing numbersproceeding toward the image plane.

The thickness of a lens element is given by the letter 2 with theappropriate subscript. For example, the thickness of lens 1 is r;,. v

The parameter n,, is the refractive index of the glass for the sodiumline. The parameter v is the v or Abbe number used with m, to identifyraglass on a glass chart. The. alphanumeric notations represent the glassdesignations ofthe Schott Glass Company of Duryea, Pa.

All dimensions are given in inches.

The focal length of the heliar plus singletat the principal position isf13.5 with f/5.6. (Overall conjugate 54.33.)

FIXED PARAMETERS VARIABLE PARAMETERS Magnification S R, R f

.99OX 25.233 13.5002 .643X 3l.l42 2l.3083 47.4095 I2.8607 .495X 34.165l9.2382 -*l2.96l9 ll.9766

The focal length of the split dagor at the principal position is f'=l3.01 with 175.6 (Overall conjugate 54.33.)

FIX ED PARAMETERS S, =0.2596 R, =2.472l S,=l .4056 R, S, =0.2I2l R=3.3748 R =3.4758 r. l.l7l8 R, r, 0.5 I76 R, =2.4I28 r, 0.3390 R.=3.5644 r, 0.348l R, =5.4504 t, 0.7374 R. 6.7029 t. 0.789l R =*3.9639 I.=SKNI8 nd=l.63854 v=55.42 l, =LFI nd=l.57309 M258 1, =BAF9 nd=l .64328v=47.96 I =BAF9 nd=l .64328 v=47.96 l, =LFI nd=l.57309 v=42.58 I =SKNI8nd=l.63854 v=55.42 SKNI8 (638554) Dense Barium Crown LFI (573426) LightFlint BAF9 (643480) Barium Flint VARIABLE PARAMETERS Magnification S. S,S. f

IX 24.096 0.650 0.l00 I358 .643X 30.174 l3.0l .495X 32.900 0.500 0.02012.07 n u RII u IX -l6.2602 2l.0526 98.0392 .643x -.495 53.9084 w76.932l 37.0370

I F4 nd=l.6l659 v=36.63 1 at IX 0.44 l =K7 nd=l.5lll2 v=60.4l tat.495X=0.35 F4 (6I7366) Flint r, at IX 0.45

K7 (511604) Crown 1, at .495x =0.40

While the invention has been described with reference to the structuresdisclosed herein, it is not confined to thedetails set forth. Forexample, the specific parameters given above to describe the heliar addlens system can vary within acceptable tolerances as is well understood.This application is intended to cover such modifications or changes asmay come within the purposes or scope of the present invention.

What is claimed is:

1. A heliar plus singlet add lens system comprising lens elements andspacings having parameters includ- FIXED PARAMETERS S,=0.5088 R =20.4682S,=0.7605 R 4.3974 S,=1.0000 R,,= 5 .4296 R,=4.1939 1,=0.7075 R,= 4.64941,=0.3684 R 1,=0.1950 R,=5.41 19 t,=0.4745 R =3.8424 1,=0.8519

1,=0.5000 l,=nd=|.62401 v=60.3 I,=nd=1.52310 v=50.9 l =nd=l.523l v=50.9l,=nd=1.52310 v=50.9 l =nd=1.62041 v=60.3 land- 152249 v=59.6

VARIABLE PARAMETERS Magnification S, R, R,,, f

.990X 25.233 13.5002 .664x 31.142 21.3083 -l7.4095 12.8607 .495X 34.16519.2382 12.9619 11.9766

wherein I through 1 define the lens elements of the heliar and I definesthe singlet with the subscripts identifying the position of the lensrelative to an object plane, the parameters R define radii of the lenselements with the subscripts identifying the surfaces of the lensproceeding with subscript l identifying the lens surface closest to theobject plane and the remaining subscripts identifying the lens surfacesdisplaced further from the object plane in ascending order, theparameters S define the spacings of the lens elements relative to eachother and the object and image planes with S, also identifying principaland add lens positions, S, defines the spacing between the object planeand the surface having radius R,, 8,, S and S, define respectively thespacings between lens I; and l the parameters 1 define the thickness ofa lens with the subscript corresponding to a lens, I, and I and I andl,,, the parameters nd define the refractive index of the glasscomprising a lens element for the sodium line and the parameters vdefine the abbe number of a glass used with nd to identify a glass on aglass chart. 2. A split dagor plus doublet add lens system comprisinglens elements and spacing having parameters including:

8 Ila-6.7029 150.7891 R,=-3.9639 !,=nd=l.63854 v=55.42 l,=nd=1.57309v=42.58 l,=nd=l.64328 1=47.96 l =nd=l.64328 v=47.96 l;=n=l.57309 v=42.58IFIIFL63854 v=55.42

VARIABLE PARAMETERS Magnification S, S, S. f

1X 24.096 0.650 0.l00 13.58 .643X 30174 13.0] .495X 32.900 0.500 0.020l2.07

1X l6.2602 2l.0526 m 98.0392 .643X .495X -53.9084 Q 76.923l 37.0370l,=nd=l.6l659 v=36.63 1-, at IX 0.44 I nFLSl l 12 M041 1, at .495X 0.35

. I; at lX 0.45

I. at .495X 0.40

wherein I, through 1,, define the lens elements of the dagor and 1define the doublet with the subscripts identifying the position of thelens relative to an object plane, the parameters R define radii of thelens elements with the subscripts identifying the surfaces of the lensproceeding with subscript l identifying the lens surface closest to theobject plane and the remaining subscripts identifying the lens surfacesdisplaced further from the object plane in ascending order, theparameters S define the spacings of the lens elements relative to eachother and the object and image planes with S, also identifying principaland add lens positions, S, defines the spacing between the object planeand the surface having radius R,, 8,, S S S and S define the spacingsrespectively between lens elements I, and l l and I I, and I I, and 1-,,and 1-, and I define respectively the spacings between lens], and l theparameters t define the thickness of a lens with the subscriptcorresponding to a lens, 1;, and 1,, and I and l the parameters nddefine the refractive index of the glass comprising a lens element forthe sodium line and the parameters v define the abbe number of a glassused with nd to identify a glass on a glass chart;

3. A lens system for a copying apparatus providing multiplemagnifications and being disposed along an optical path between fixedobject and image planes in which respectively an original to be copiedand a recording medium are located, said lens system includmg:

a basic lens group disposed for movement along said optical path betweenextreme positions and having an intermediate position therebetween inwhich said basic lens group is in focus relative to said ohject andimage planes at an intermediate magnification,

add lens elements for adding to said basic lens group, said add lenselements being movable into and out of said optical path for selectivecombination with said basic lens group,

at least one of said add lens elements combining in a first combinationwith said basic lens group when the same is at a position toward saidobject plane relative to' said intermediate position, said firstcombination being in focus relative to said object and image planes at afirst magnification greater than said intermediate magnification,

at least one of said add lens elements combining in a second combinationwith said basic lens group when the same is at a position toward saidimage plane relative to said intermediate position, said secondcombination being in focus relative to said object and image planes at asecond magnification smallerthan said intermediate magnification.

4. The system of claim 3 wherein said basic lens group includes a splitDagor lens.

5. The system of claim 3 wherein said add lens elements include lensdoublets for inclusion with said basic lens group when located atbalanced add lens positions.

6. A lens system for a copying apparatus providing multiplemagnifications and being disposed along an optical path between fixedobject and image planes in which respectively an original to be copiedand a recording medium are located, said lens system includa basic lensgroup disposed for movement along said optical path between extremepositions and having an intermediate position therebetween,

add lens elements for subtracting from or adding to said basic lensgroup, said add lens elements being movable into and out of said opticalpath for selective combination with said basic lens group,

at least one of said add lens elements combining in an intermediatecombination with said basic lens group when the same is at saidintermediate position, said intermediate combination being in focusrelative to said object and image planes at an intermediatemagnification, 7

said basic lens group being in focus relative to said object and imageplanes at a first magnification greater than said intermediatemagnification when said basic lens group is at a position toward saidobject plane relative to said intermediate position,

at least one of said add lens elements combining in a second combinationwith said basic lens group when the same is at a position toward saidimage plane relative to said intermediate position, said secondcombination being in focus relative to said object and image planes at amagnification smaller than said intermediate magnification.

7. The system of claim 6 wherein said basic lens group includes anon-symmetrical heliar lens.

II i t

1. A heliar plus singlet add lens system comprising lens elements andspacings having parameters including: FIXED PARAMETERS S2 0.5088 R6-20.4682 S3 0.7605 R7 4.3974 S4 1.0000 R8 -5.4296 R1 4.1939 t1 0.7075 R2-4.6494 t2 0.3684 R3 infinity t3 0.1950 R4 -5.4119 t4 0.4745 R5 3.8424t5 0.8519 t6 0.5000 l1 nd 1.62401 v 60.3 l2 nd 1.52310 v 50.9 l3 nd1.52310 v 50.9 l4 nd 1.52310 v 50.9 l5 nd 1.62041 v 60.3 l6 nd 1.52249 v59.6 VARIABLE PARAMETERS Magnification S1 R9 R10 f''.990 X 25.23313.5002 .664 X 31.142 -21.3083 -17.4095 12.8607 .495 X 34.165 19.2382-12.9619 11.9766 wherein l1 through l5 define the lens elements of theheliar and l6 defines the singlet with the subscripts identifying theposition of the lens relative to an object plane, the parameters Rdefine radii of the lens elements with the subscripts identifying thesurfaces of the lens proceeding with subscript 1 identifying the lenssurface closest to the object plane and the remaining subscriptsidentifying the lens surfaces displaced further from the object plane inascending order, the parameters S define the spacings of the lenselements relative to each other and the object and image planes with S1also identifying principal and add lens positions, S1 defines thespacing between the object plane and the surface having radius R1, S2,S3, and S4 define respectively the spacings between lens l2 and l3, theparameters t define the thickness of a lens with the subscriptcorresponding to a lens, l3 and l4, and l5 and l6, the parameters nddefine the refractive index of the glass comprising a lens element forthe sodium line and the parameters v define the abbe number of a glassused with nd to identify a glass on a glass chart.
 2. A split dagor plusdoublet add lens system comprising lens elements and spacing havingparameters including: FIXED PARAMETERS S2 0.2596 R8 -2.4721 S3 1.4056 R9Infinity S4 0.2121 R10 -3.3748 R1 3.4758 t1 1.1718 R2 Infinity t2 0.5176R3 2.4128 t3 0.3390 R4 3.5644 t4 0.3481 R5 5.4504 t5 0.7374 R6 -6.7029t6 0.7891 R7 -3.9639 l1 nd 1.63854 v 55.42 l2nd 1.57309 v 42.58 l3 nd1.64328 v 47.96 l4 nd 1.64328 v 47.96 l5 nd 1.57309 v 42.58 l6 nd1.63854 v 55.42 VARIABLE PARAMETERS Magnification S1 S5 S6 f''1 X 24.0960.650 0.100 13.58 .643 X 30.174 13.01 .495 X 32.900 0.500 0.020 12.07R11 R12 R13 R14 1 X -16.2602 -21.0526 Infinity -98.0392 .643 X .495 X-53.9084 Infinity 76.9231 -37.0370 l7 nd 1.61659 v 36.63 t7 at 1 X 0.44l8 nd 1.51112 v 60.41 t7 at .495 X 0.35 t8 at 1 X 0.45 t8 at .495 X 0.40wherein l1 through l6 define the lens elements of the dagor and l7 8define the doublet with the subscripts identifying the position of thelens relative to an obJect plane, the parameters R define radii of thelens elements with the subscripts identifying the surfaces of the lensproceeding with subscript 1 identifying the lens surface closest to theobject plane and the remaining subscripts identifying the lens surfacesdisplaced further from the object plane in ascending order, theparameters S define the spacings of the lens elements relative to eachother and the object and image planes with S1 also identifying principaland add lens positions, S1 defines the spacing between the object planeand the surface having radius R1, S2, S3, S4, S5 and S6 define thespacings respectively between lens elements l2 and l3, l3 and l4, l4 andl5, l6 and l7, and l7 and l8, define respectively the spacings betweenlens l2 and l3, the parameters t define the thickness of a lens with thesubscript corresponding to a lens, l3 and l4, and l5 and l6, theparameters nd define the refractive index of the glass comprising a lenselement for the sodium line and the parameters v define the abbe numberof a glass used with nd to identify a glass on a glass chart.
 3. A lenssystem for a copying apparatus providing multiple magnifications andbeing disposed along an optical path between fixed object and imageplanes in which respectively an original to be copied and a recordingmedium are located, said lens system including: a basic lens groupdisposed for movement along said optical path between extreme positionsand having an intermediate position therebetween in which said basiclens group is in focus relative to said object and image planes at anintermediate magnification, add lens elements for adding to said basiclens group, said add lens elements being movable into and out of saidoptical path for selective combination with said basic lens group, atleast one of said add lens elements combining in a first combinationwith said basic lens group when the same is at a position toward saidobject plane relative to said intermediate position, said firstcombination being in focus relative to said object and image planes at afirst magnification greater than said intermediate magnification, atleast one of said add lens elements combining in a second combinationwith said basic lens group when the same is at a position toward saidimage plane relative to said intermediate position, said secondcombination being in focus relative to said object and image planes at asecond magnification smaller than said intermediate magnification. 4.The system of claim 3 wherein said basic lens group includes a splitDagor lens.
 5. The system of claim 3 wherein said add lens elementsinclude lens doublets for inclusion with said basic lens group whenlocated at balanced add lens positions.
 6. A lens system for a copyingapparatus providing multiple magnifications and being disposed along anoptical path between fixed object and image planes in which respectivelyan original to be copied and a recording medium are located, said lenssystem including: a basic lens group disposed for movement along saidoptical path between extreme positions and having an intermediateposition therebetween, add lens elements for subtracting from or addingto said basic lens group, said add lens elements being movable into andout of said optical path for selective combination with said basic lensgroup, at least one of said add lens elements combining in anintermediate combination with said basic lens group when the same is atsaid intermediate position, said intermediate combination being in focusrelative to said object and image planes at an intermediatemagnification, said basic lens group being in focus relative to saidobject and image planes at a first magnification greAter than saidintermediate magnification when said basic lens group is at a positiontoward said object plane relative to said intermediate position, atleast one of said add lens elements combining in a second combinationwith said basic lens group when the same is at a position toward saidimage plane relative to said intermediate position, said secondcombination being in focus relative to said object and image planes at amagnification smaller than said intermediate magnification.
 7. Thesystem of claim 6 wherein said basic lens group includes anon-symmetrical heliar lens.